An expert witness in a case of alleged racial discrimination in a state university school of nursing
introduced a regression of the determinants of Salary of each professor for each year during an
8-year period (n = 423) with the following results, with dependent variable Year (year in which
the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if
individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise).
Interpret these results.
Variable Coefficient t p
Intercept −3,816,521 −29.4 .000
Year 1,948 29.8 .000
YearHire −826 −5.5 .000
Race −2,093 −4.3 .000
Rank −6,438 −22.3 .000
R2 = 0.811 R2
adj
= 0.809 s = 3,318
To interpret the results of the regression analysis, we need to look at each coefficient and its associated statistics.
1. Intercept: The intercept coefficient (-3,816,521) represents the estimated average salary in the base year when all other predictors (YearHire, Race, Rank) are set to zero. In this case, the intercept is not particularly meaningful since it is unlikely to have a Year value that is negative.
2. Year: The coefficient for Year (1,948) indicates the average change in salary for each increase in one unit of Year. In this case, it means that every year, on average, the salary increases by $1,948.
3. YearHire: The coefficient for YearHire (-826) suggests that, on average, for each additional year of hiring, the salary decreases by $826. This might indicate that individuals who were hired more recently have lower salaries compared to those hired earlier.
4. Race: The coefficient for Race (-2,093) implies that, on average, being black is associated with a $2,093 decrease in salary compared to individuals who are not black. This suggests a potential racial wage gap within this university's school of nursing.
5. Rank: The coefficient for Rank (-6,438) indicates that, on average, being an assistant professor is associated with a $6,438 decrease in salary compared to other ranks (such as associate or full professor). This implies that individuals with higher ranks tend to have higher salaries.
R-squared (R²) is a measure of how well the regression model fits the data. In this case, the R² value is 0.811, indicating that the predictors (Year, YearHire, Race, Rank) explain approximately 81.1% of the variation in salary among the professors.
Adjusted R-squared (R²_adj) takes into account the number of predictors in the model. In this case, the R²_adj value is 0.809, which is very close to the R² value.
The standard error (s) is a measure of the average deviation of the actual salary values from the predicted values by the regression model. In this case, the standard error is 3,318, which indicates the average deviation of the observed salaries from the predicted salaries is approximately $3,318.
In summary, based on the regression analysis, we can infer that as the years increase, on average, the salary also increases. However, being hired later, being black, and having a lower rank (assistant professor) are associated with lower salaries in the state university's school of nursing. These findings suggest the presence of potential racial discrimination and disparities in salary within the institution.